“I think he embarrassed himself,” Wallace told "Daily Briefing" host Dana Perino. “First of all, it was more of an argument than it was a question. He was disrespectful to his colleagues in asking repeated questions and, thereby, making it harder for them to get in a question. Then the President of the United States told him to sit down, and he refused, and he kept talking.”

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“I do know a lot of Jim Acosta’s colleagues are very frustrated with him," reported Perino, who once served as White House press secretary under former President George W. Bush.

"We do have to stick together," he added. "But I gotta say, Jim Acosta makes it awfully hard to have journalistic solidarity on something like this.”

As the interview ended, Wallace asked what CNN's mission was in terms of whether to report the story or be the story.

“What do the bosses at CNN see as their mission? In this particular case is it to cover the news, or is it to make a scene?”

Several press organizations, including the White House Correspondents Association, have voiced their support for Acosta.

"Journalists may use a range of approaches to carry out their jobs and the WHCA does not police the tone or frequency of the questions its members ask of powerful senior government officials, including the President," said WHCA president Olivier Knox in a statement on Wednesday. "Such interactions, however uncomfortable they may appear to be, help define the strength of our national institutions. We urge the White House to immediately reverse this weak and misguided action."

Wallace had also criticized Acosta on Wednesday afternoon after the press conference, stating the CNN reporter had "embarrassed himself."